S. V. Matveev, “Tabulation of three-dimensional manifolds”, Russian Math. Surveys, 60:4 (2005), 673

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Russian Mathematical Surveys, 2005, Volume 60, Issue 4, Pages 673–698
DOI: https://doi.org/10.1070/RM2005v060n04ABEH003673 (Mi rm1446)

This article is cited in 28 scientific papers (total in 28 papers)

Tabulation of three-dimensional manifolds

S. V. Matveev

Chelyabinsk State University

English version PDF (456 kB) Citations (28) Russian version article

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DOI: https://doi.org/10.1070/RM2005v060n04ABEH003673

Abstract: The formation of tables of three-dimensional manifolds requires the development and computer realization of two algorithms: the listing algorithm and the recognition algorithm. In this paper the theoretical foundations of these algorithms are presented and a survey of results concerning the practical tabulation of three-dimensional manifolds is given.

Received: 11.05.2005

Bibliographic databases:

Document Type: Article

UDC: 515.16

MSC: Primary 57N10; Secondary 57M27, 57M15, 57N05, 57-04

Language: English

Original paper language: Russian

Citation: S. V. Matveev, “Tabulation of three-dimensional manifolds”, Russian Math. Surveys, 60:4 (2005), 673–698

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/rm1446

https://doi.org/10.1070/RM2005v060n04ABEH003673

https://www.mathnet.ru/eng/rm/v60/i4/p97

This publication is cited in the following 28 articles:

Marc Lackenby, Jessica S. Purcell, “The triangulation complexity of elliptic and sol 3-manifolds”, Math. Ann., 2024
Marc Lackenby, Jessica S Purcell, “The triangulation complexity of fibred 3–manifolds”, Geom. Topol., 28:4 (2024), 1727
Lee Lindblom, Oliver Rinne, Nicholas W. Taylor, “Building three-dimensional differentiable manifolds numerically”, Journal of Computational Physics, 460 (2022), 110957
S. V. Matveev, V. V. Tarkaev, “Recognition and tabulation of $3$ -manifolds up to complexity $13$ ”, Chebyshevskii sb., 21:2 (2020), 290–300
A. Yu. Vesnin, S. V. Matveev, E. A. Fominykh, “New aspects of complexity theory for 3-manifolds”, Russian Math. Surveys, 73:4 (2018), 615–660
A. Yu. Vesnin, “Right-angled polyhedra and hyperbolic 3-manifolds”, Russian Math. Surveys, 72:2 (2017), 335–374
A. Yu. Vesnin, T. A. Kozlovskaya, “Brieskorn manifolds, generated Sieradski groups, and coverings of lens space”, Proc. Steklov Inst. Math. (Suppl.), 304, suppl. 1 (2019), S175–S185
A. Yu. Vesnin, V. G. Turaev, E. A. Fominykh, “Complexity of virtual 3-manifolds”, Sb. Math., 207:11 (2016), 1493–1511
A. Yu. Vesnin, V. G. Turaev, E. A. Fominykh, “Three-dimensional manifolds with poor spines”, Proc. Steklov Inst. Math., 288 (2015), 29–38
A. Yu. Vesnin, E. A. Fominykh, “Two-sided bounds for the complexity of hyperbolic three-manifolds with geodesic boundary”, Proc. Steklov Inst. Math., 286 (2014), 55–64
V. V. Tarkaev, E. A. Fominykh, “Verkhnie otsenki slozhnosti dopolnitelnykh prostranstv nekotorykh kruzhevnykh uzlov”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 6:3 (2014), 50–52
Jaco W., Rubinstein J.H., “Inflations of Ideal Triangulations”, Adv. Math., 267 (2014), 176–224
William Jaco, J. Hyam Rubinstein, Stephan Tillmann, “
$\mathbb Z _2$
-Thurston norm and complexity of 3-manifolds”, Math. Ann, 2012
A. Yu. Vesnin, E. A. Fominykh, “On complexity of three-dimensional hyperbolic manifolds with geodesic boundary”, Siberian Math. J., 53:4 (2012), 625–634
Casali M.R., Cristofori P., Mulazzani M., “Complexity Computation for Compact 3-Manifolds via Crystallizations and Heegaard Diagrams”, Topology Appl., 159:13, SI (2012), 3042–3048
Martelli B., “Four-manifolds with Shadow-complexity Zero”, Internat. Math. Res. Notices, 2011 (2011), 1268–1351
E. A. Fominykh, “Dehn surgeries on the figure eight knot: an upper bound for complexity”, Siberian Math. J., 52:3 (2011), 537–543
A. Yu. Vesnin, S. V. Matveev, E. A. Fominykh, “Slozhnost trekhmernykh mnogoobrazii: tochnye znacheniya i otsenki”, Sib. elektron. matem. izv., 8 (2011), 341–364
Burton B.A., “Detecting Genus in Vertex Links for the Fast Enumeration of 3-Manifold Triangulations”, Issac 2011: Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation, ed. Leykin A., Assoc Computing Machinery, 2011, 59–66
Martelli B., “Complexity of PL manifolds”, Algebr. Geom. Topol., 10:2 (2010), 1107–1164

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	849
Russian version PDF:	323
English version PDF:	62
References:	105
First page:	3

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